As you know, all optical filters absorb some light hence require an increased exposure to compensate. The magnitude of this increase is universally called the “filter factor”. This value is likely published by the filter manufacturer or you can derive it by making as simple bracketing test.
Once the filter factor is known, we can use it as a multiplier. Suppose a shot of a vista works out to f/16 @ 1/250 of a second. Now you mount a neutral density filter with a filter factor of 8. What is the revised exposure? We calculate by applying the filter factor to the shutter speed thus: 1/125 X 8 = 1/125 X 8/1 = 8/125 = 1/15. If this seems difficult, likely you are a bit rusty when it comes to manipulating fractions.
Table of Filter factors:
1 stop absorption = filter factor 2
2 stop absorption = filter factor 4
3 stop absorption = filter factor 8
4 stop absorption = filter factor 16
5 stop absorption = filter factor 32
They key is: The f-stop is a 2x increment, a doubling of halving of the amount of exposing energy. The basic equation for exposure is E=IT where E=exposure, I = the exposing radiation, and T=the duration of the exposure.
Sorry -- French is Greek to me!
Stated a little differently:
A filter factor is a modifier. Once the filter factor is known, to compute a revised shutter speed, multiply the time of exposure by the filter factor. One can modify the ISO by dividing it by the filter factor. One can modify the f-number by dividing it by the square root of the filter factor.
Filters absorb a quota of the exposing light. It is customary to express the needed correction in terms of f-stops. By custom, the f-stop is defined as a 2X change in exposing energy. Thus a filter that attenuates by 50% requires + 1 f-stop compensation. Another way to express this attenuation is via a “filter factor = 2 elevated to x power. The x power is the number of f-stops attenuated. Photo scientist express filter attenuation based on its “opacity” = insistent light divided by amount of light that traversed. Optical density is the logarithm base 10 of the opacity.
1/6 f-stop = 2^0.16 = 1.1 filter factor = optical density 0.05
1/3 f-stop = 2^0.33 = 1.3 filter factor = optical density 0.10
1/2 f-stop = 2^0.5= 1.4 filter factor = optical density 0.15
2/3 f-stop = 2^0.66 = 1.6 filter factor = optical density 0.20
1 f-stop = 2^1 = 2 filter factor = optical density 0.30
2 f-stops = 2^2 = 4 filter factor = optical density 0.60
3 f-stop = 2^3 = 8 filter factor = optical density 0.90
4 f-stops = 2^4 = 16 filter factor = optical density 0.90
5 f-stop = 2^5 = 32 filter factor = optical density 1.20
6 f-stops = 2^6 = 64 filter factor = optical density 1.50